bettatantalo wrote:

Drinks A and B are mixtures of lemon and orange juices. The ratio of lemon to orange juice is 1:3 in drink A. In drink B, the ratio of lemon to orange juices is 5 : 3. If drink A is mixed with drink B to form drink C in the ratio of 4 : 1, what is the ratio of lemon to orange juice in drink c?

a) 1 : 1

b) 2 : 1

c) 3 : 2

d) 13 : 27

e) 15 : 19

source gmat tutor

Beqa chose an excellent method. +1

We can also find amounts of each juice in a 4:1 mix, and set them in a ratio

To find concentration of, say, OJ in A,

sum the ratio parts.

Concentration = \(\frac{part}{total}=\frac{L}{L+OJ}\)

A mix: \(\frac{L}{OJ}=\frac{1}{3}\)

Total parts: (1 + 3) = 4

A, concentration of \(L = \frac{1}{4}\)

A, concentration of \(OJ=\frac{3}{4}\)

B mix: \(\frac{L}{OJ}=\frac{5}{3}\)

Total parts: (5 + 3) = 8

B, concentration of \(L = \frac{5}{8}\)

B, concentration of \(OJ=\frac{3}{8}\)

Drink A is mixed with drink B in the ratio of 4:1 to form drink C

So the amount of A in the resultant drink C is 4 times as much as B

Lemon juice only in 4A + 1B?

\((4)(\frac{1}{4})+(1)(\frac{5}{8})=\)

\((1+\frac{5}{8})=(\frac{8}{8}+\frac{5}{8})=\frac{13}{8}\)

Orange juice only in 4A+1B?

\((4)(\frac{3}{4})+(1)(\frac{3}{8})=\)

\((3+\frac{3}{8})=(\frac{24}{8}+\frac{3}{8})=\frac{27}{8}\)

Ratio of lemon juice to orange juice in C?

C = mix of 4A and 1B, as above

\(\frac{L}{OJ}=\frac{(\frac{13}{8})}{(\frac{27}{8})}=(\frac{13}{8}*\frac{8}{27})=\frac{13}{27}\)

Answer D